Editing Factorization (section)

===History of factorization of expressions===

The systematic use of algebraic manipulations for simplifying expressions (more specifically [[equation]]s) may be dated to 9th century, with [[Muhammad ibn Musa al-Khwarizmi|al-Khwarizmi]]'s book ''[[The Compendious Book on Calculation by Completion and Balancing]]'', which is titled with two such types of manipulation.

However, even for solving [[quadratic equation]]s, the factoring method was not used before [[Thomas Harriot|Harriot]]'s work published in 1631, ten years after his death.<ref>In {{citation|first=Vera|last=Sanford|title=A Short History of Mathematics|year=2008|orig-year=1930|publisher=Read Books|isbn=9781409727101}}, the author notes "In view of the present emphasis given to the solution of quadratic equations by factoring, it is interesting to note that this method was not used until Harriot's work of 1631".</ref> In his book ''Artis Analyticae Praxis ad Aequationes Algebraicas Resolvendas'', Harriot drew tables for addition, subtraction, multiplication and division of [[monomial]]s, [[binomial (polynomial)|binomial]]s, and [[trinomial]]s. Then, in a second section, he set up the equation {{math|1=''aa'' − ''ba'' + ''ca''  = + ''bc''}}, and showed that this matches the form of multiplication he had previously provided, giving the factorization  {{math|(''a'' − ''b'')(''a'' + ''c'')}}.<ref>{{cite book | last=Harriot | first=T. | title=Artis Analyticae Praxis ad Aequationes Algebraicas Resolvendas | publisher=Apud Robertum Barker, typographum regium | year=1631 | url=https://books.google.com/books?id=771CAAAAcAAJ | language=la | mode=cs2}}</ref>